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A tautology is a statement which is always true.

What is the name for a statement which is always false?

Is it correct that a statement is either tautology, the false counterpart of tautology, or contingent?

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    Contradiction.................. Sep 27, 2023 at 9:40
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    Politics.......
    – Scott Rowe
    Sep 27, 2023 at 10:50
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    See Copi, page 287-288 for the definitions of tautology, contradiction and contingent. Sep 27, 2023 at 13:11
  • Contradiction is the most common. Some texts use 'self-contradiction' rather than just contradiction. You could also say 'logical falsehood', by way of contrast with logical truth.
    – Bumble
    Sep 29, 2023 at 3:11

3 Answers 3

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A tautology is not "a statement that is always true". In such case, 1>0 would be a tautology, but it is not.

A tautology is a logical structure that is true just by its logical form, not by its meaning, like on the previous example. So, "a=a" is true because of the logical structure, not because of the value of a.

The opposite would be a statement that is false due to its structure. The closest form to that is a contradiction in the structure, which has not a name as such. The term contradiction might cover it, though.

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I believe the false counterpart for a tautology is a contradiction. When using truth tables to investigate statements, if the outcome is always true, the statement is a tautology. If it's always false, it's a contradiction.If it's a mixture of both, then it's neither a tautology nor a contradiction.

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    +1 First to the egg. It is indeed a contradiction.
    – J D
    Sep 27, 2023 at 13:49
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While the answer has been given, it might help to think in terms truth tables. In some truth table, if a proposition always evaluates to true given every possible entry, you have a tautology. Contradictions arise when the table always evaluates to false, and tables that present with a mix of true and false are contingent propositions. Contingent propositions give rise to another flavor of logic called modal logic where necessary and possible operators are introduced in statements.

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